IT3_2005-6_paper_v2

IT3_2005-6_paper_v2 - INFORMATION THEORY 3 MATH 34600 FINAL...

Info iconThis preview shows pages 1–3. Sign up to view the full content.

View Full Document Right Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: INFORMATION THEORY 3 MATH 34600 FINAL EXAM PAPER 2005/06 This paper contains three questions; each is worth 25 marks. A candidate’s two best answers will be used for assessment. Time given is 2(?) hours. Date of the exam: dd/mm/2005 ... am to ... pm. A calculator of the approved type is allowed. 1 1. Consider the source X with alphabet A = { α,β,γ,δ,ε,ϕ } and probability distribution P X : x α β γ δ ε ϕ P X ( x ) .3 .2 .15 .125 .125 .1 (a) State Kraft’s condition for the existence of a prefix-free binary code for a general alphabet X with supposed codeword lengths ℓ x (inte- gers), x ∈ X . [4 marks] (b) Construct the Shannon-Fano code for the source X , writing down the required code word lengths first. [6 marks] (c) Calculate the expected length of your code, and the entropy of the source X . [4 marks] (d) Explain the significance of the entropy in the context of Shannon’s source coding theorem. Be careful to define any notation and termi- nology you introduce. [3 marks] (e) Still referring to Shannon’s source coding theorem: Explain in words the difference of performance of your code constructed in (b) and the asymptotically optimal source code. [3 marks] (f) Can you improve the expected length of the code you constructed in part (b)? If so, show how to do this. (Hint: is the Kraft inequalitypart (b)?...
View Full Document

This note was uploaded on 12/01/2010 for the course ADLAC 1023 at Stanford.

Page1 / 4

IT3_2005-6_paper_v2 - INFORMATION THEORY 3 MATH 34600 FINAL...

This preview shows document pages 1 - 3. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online